We study the achievable rate regions of full-duplex links in the single- and multi-channel cases (in the latter case, the channels are assumed to be orthogonal, e.g., OFDM). We present analytical results that characterize the uplink and downlink rate region and efficient algorithms for computing rate pairs at the region's boundary. We also provide near-optimal and heuristic algorithms that “convexify” the rate region when it is not convex. The convexified region corresponds to a combination of a few full-duplex rates (i.e., to time sharing between different operation modes). The algorithms can be used for theoretical characterization of the rate region as well as for resource (time, power, and channel) allocation with the objective of maximizing the sum of the rates when one of them (uplink or downlink) must be guaranteed (e.g., due to QoS considerations). We numerically illustrate the rate regions and the rate gains (compared with time division duplex) for various channel and cancellation scenarios. The analytical results provide insights into the properties of the full-duplex rate region and are essential for future development of scheduling, channel allocation, and power control algorithms.